But the government is rejecting that, and it is strengthening discrimination laws to remove any opportunity for schools to discriminate.

"Our government does not support expulsion of students from religious non-state schools on the basis of their sexuality," Prime Minister Scott Morrison said in a statement.

"I also know that this view is widely shared by religious schools and communities across the country." The coalition government is working on amendments it plans to make law within the next two weeks.

"I will be taking action to ensure amendments are introduced as soon as practicable to make it clear that no student of a non-state school should be expelled on the basis of their sexuality," Mr Morrison said.

The issue arose in a controversial review into religious freedoms, led by former Liberal minister Philip Ruddock, that called for stronger rights for schools to reject gay staff and students.

Protection of religious beliefs already exists in almost every state and territory jurisdiction, except NSW and South Australia.

Mr Morrison hit out at "misreporting" of the Ruddock review, which he said actually proposed restricting the rights of schools to expel students based on religious doctrine.

"I will be writing to the Opposition Leader Bill Shorten to invite him to work with the government on a bipartisan basis to provide certainty in this area," Mr Morrison said.

Former Federal Liberal MP Phillip Ruddock. Picture: Dan Himbrechts

Mr Shorten also wrote to the prime minister on Friday, offering his support for changes to the Sex Discrimination Act.

"To remove the exemptions that currently allow religious schools to discriminate against children on the basis of their sexual orientation and gender identity," Mr Shorten wrote.

He also called on the government to release the full Ruddock review so the public can have a say.

Mr Morrison said the government was still working through the report, and it would talk to Labor and the public about further issues in the future. The review was commissioned after last year's same-sex marriage plebiscite, to appease conservatives who feared the change would restrict their religious freedoms.

Catholic Archbishop Mark Coleridge said the church had not sought concessions to discriminate against students or staff based on their sexuality. Islamic Council of Victoria spokesman Adel Salman told Network Ten religious schools should be able to teach their values, and staff and students should abide by them at school.